A conducting sphere at potential V0 is half embedded in linear dielectric material of susceptibility Xe, which occupies the region z (a) Write down the formula for the proposed potential V(r), in terms of V0, R, and r. Use it to determine the field, the polarization, the bound charge, and the free charge distribution on the sphere.

(b) Show that the total charge configuration would indeed produce the potential V(r).

(c) Appeal to the uniqueness theorem in Prob. 4.35 to complete the argument.

(d) Could you solve the configurations in Fig. 4.36 with the same potential? If not, explainwhy.

1000 R